Why do bars cut people off after awhile? Are they afraid I'll drink them out of business or hog all the booze?

A little story:
Person decides to go to a bar. Let's call this person Pat (a non-gender specific name)

Pat drinks until Pat can no longer walk straight.
Pat decides to get behind the wheel and drive home.
Pat has a accident and dies in the wreckage. (This time, luckily, Pat didn't kill any 'innocent' people along with Pat's own self)
Pat's family are devastated over their loss. Understandably.

But some time after the funeral, Pat's family decides it's 'unfair' that they were made to suffer with this horrible pain of Pat's death, and they decide that someone ought to be held accountable for Pat's poor decision making skills.
So Pat's family does some digging, and discover that Pat spent the whole night drinking at O'Sullivan's Bar on the night of the accident.
They figure that the bar ought to be held responsible for the inebriated state Pat was in when Pat left their establishment.
So they fight and rally, and they succeed in suing the establishment for 'allowing' Pat to become so drunk.

Now, bars are actually held liable for the safety of their patrons UNTIL THEY ARE SOBER again.

That is why bars cut people off.
They do not wish to be held liable for some peoples' idiotic choices and irresponsible behaviours.
And they (understandably) wish to keep their profits IN THEIR BANK ACCOUNTS instead of paying for lawsuits against stupid people who insist on driving drunk.

*whew*
*climbs down off my soapbox*
I'm just sayin'
😉

There are laws called “Dram Shop Acts” which hold a business which sells alcoholic drinks (such as a bar) or a host who serves liquor to a drinker who is obviously intoxicated or close to it, strictly liable to anyone injured by the drunken patron or guest (some States hold businesses to a higher standard than the host of a party in this regard).
@Greenbare and @bijouxbroussard are correct....the bars do this to avoid being held responsible for injury caused by someone who was served when intoxicated or nearly intoxicated (even when that injury is suffered by the drunk person).
It is not worth it to risk that much responsibility in order to sell a couple of additional drinks.

Uhhhhh I'm pretty sure they just want you to leave.

They don't want to be responsible for alcohol poisoning, drunk driving, etc. And in this litigious society people have filed suit against clubs, bars and even bartenders when someone has gotten too drunk.

They don't want to be liable and sued.

Have you ever been with severely drunk people? Not a fun experience